volumes

[jeca86]

find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1), and the x-axis.

can i get a walk through?

 

[Euler]

Antiderive x^2 and get 1/3x^3. Find where the left and right bounds are for the x^2 function (these will be the zeroes). Apply the fundamental theorem of calculus: g(b)-g(a) to get your answer. Do the same thing with the next one.

 

[galactus]

One approach would be to integrate the region \(\displaystyle x^{2}-(2x-1)\)

from 0 to 1, then subtract the triangle area formed by the line crossing

the x-axis and intersecting the parabola at x=1.